p-Linear schemes for sequences modulo p^r

2022/11/28 by Frits Beukers, Beukers, Frits
Computer Science · Mathematics · #11B50 #11B85 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2211.15240

openalex publication_date 2022/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Many interesting combinatorial sequences, such as Apéry numbers and Franel numbers, enjoy the so-called Lucas property modulo almost all primes p. Modulo prime powers p^r such sequences have a more complicated behaviour which can be described by matrix versions of the Lucas property called p-linear schemes. They are examples of finite p-automata. In this paper we construct such p-linear schemes and give upper bounds for the number of states which, for fixed r, do not depend on p.

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